Robust Control And Fault Detection For Stochastic Jump Systems

In the practical process, many control systems inevitably encounter various uncertainties and external disturbances, and such factors usually impact the systems in a stochastic way. To establish the precise stochastic model, we should fully consider these affecting factors. As a special class of stochastic systems, the research of Markov jump systems gives an impetus to stochastic control, and these discussions enrich the research and control theory. Moreover, the application of Markov jump systems are more comprehensive, for instance, manufacturing systems, bio-systems, economic systems, electrical power systems and network communication systems, etc. Therefore, the study of stochastic jump systems is very important and can possess real significance.The main work of this dissertation investigates stochastic jump systems, including such systems subject to uncertainties, time delays and nonlinearities. By using the Lyapunov-Krosovskii functional theory, the research contents mainly relate to finite-time controller design, observer-based robust controller design, output regulator design and fault detection, etc. The controller design approaches are based on feedback control theory and all results can be reduced to a feasible problem of linear matrix inequalities (LMIs). With the aid of the interior-point algorithm, the solutions of LMIs can be easily obtained. The studied problems are feasible and are of innovation. The research works of this dissertation are divided into six chapters, and the main contents are as follows:(1). The problems for the analysis and synthesis of jump systems are considered. For the continuous system and discrete system, sufficient conditions that the solution of finite time stable and stabilization controller is existed are respectively given and proved by using the constructed Lyapunov-Krasovskii functional approaches and LMIs techniques. And the main results are extended to jump systems with uncertainties, time-delays and nonlinearities, and the designed approaches include robust control, H?control and fuzzy control. Simulation results illustrate the effectiveness of the developed approaches.(2). The H?control, passive control and finite-time H?control problem of a class of uncertain time-delay jump linear systems are respectively studied. An observer-based optimized robust controller is designed for a given system with energy bounded noise inputs. Based on the robust control theory, the sufficient conditions for the existence of mode-dependent H?controller, passive controller and finite-time H?controller are respectively given by analyzing the reconstructed observer systems. By constructing proper Lyapunov-Krasovskii functional and applying LMIs, the design problem of the controllers are derived and described as optimization ones. Simulation results demonstrate that the presented observer-based optimized robust controller makes the systems stochastically stable, have better ability of tracking state and restraining disturbances, and satisfies the presented norm index.(3). Using the analytic model-based state estimation approach, the fault detection schemes of linear and nonlinear jump system with external disturbances and unknown faults are respectively studied. By constructing proper Lyapunov-Krasovskii functional and applying LMIs technique, sufficient conditions for the solvability of the fault detection problem and the optimized design approach are presented and proved. The designed observer and filter make the systems stochastically stable, have better ability of restraining disturbances, and detect the faults sensitively.(4). The output regulation problems of jump systems are respectively considered by applying state-feedback and error feedback schemes. With the extension of output regulation to stochastic control, sufficient conditions are obtained continuous-time and discrete-time jump system based on stochastic Lyapunov-Krasovskii functional. In order to ensure the relaxed solutions of the regulation equations, we described the problems as semi-definite programming (SDP) approaches via disciplined convex optimization. The resulting closed-loop system is guaranteed to be stochastically stable and the output tracking is achieved almost asymptotically. Moreover, the output regulation error almost asymptotically converges to zero. Simulation result is also given to illustrate the performance and effectiveness of the proposed approach.Finally, the conclusions and research prospects are given. Furthermore, some further research work and existing issues for Markov jump systems are also pointed out.